Question

2(x+1) - (x-2)>3(x-2) AJUDEM

Answer 1

Dada a inequação:

$\mathsf{2\left(x+1\right)-\left(x-2\right)\ \textgreater \ 3\left(x-2\right)}$

Resolvendo as multiplicações:

$\mathsf{2x+2-\left(x-2\right)\ \textgreater \ 3\left(x-2\right)}\\\\\mathsf{2x+2-x+2\ \textgreater \ 3\left(x-2\right)}\\\\\mathsf{2x+2-x+2\ \textgreater \ 3x-6}\\\\\mathsf{2x-x+2+2\ \textgreater \ 3x-6}\\\\\mathsf{x+4\ \textgreater \ 3x-6}\\\\\mathsf{x-3x\ \textgreater \ -6-4}\\\\\mathsf{-2x\ \textgreater \ -10}$

Multiplicando os dois termos por -1 e invertendo o sinal da inequação:

$\mathsf{2x\ \textless \ 10}\\\\\mathsf{x\ \textless \ \dfrac{10}{2}}\\\\\mathsf{x\ \textless \ 5}$

Portanto o conjunto solução sera:

$\boxed{\mathsf{S=\left\{x\in \mathbb{R}\:,\:x\ \textless \ 5\right\}}}\: \: \checkmark$